{
  "id": "2106.14558",
  "version": "v1",
  "published": "2021-06-28T10:29:53.000Z",
  "updated": "2021-06-28T10:29:53.000Z",
  "title": "Diophantine problems related to cyclic cubic and quartic fields",
  "authors": [
    "Szabolcs Tengely",
    "Maciej Ulas"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We are interested in solving the congruences $f^3+g^3+1\\equiv 0\\pmod{fg}$ and $f^4-4g^2+4\\equiv 0\\pmod{fg}$ in polynomials $f, g$ with rational coefficients. Moreover, we present results of computations of all integer points on certain one parametric curves of genus 1 and 3, related to cubic and quartic fields, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-28T10:29:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quartic fields",
      "cyclic cubic",
      "diophantine problems",
      "rational coefficients",
      "integer points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}